On the distribution of a product of N Gaussian random variables

Publikationstyp
Conference Paper
Publikationsdatum
2017-08
Sprache
English
Author
Stojanac, Åeljka 
Suess, Daniel 
Kliesch, Martin 
TORE-URI
http://hdl.handle.net/11420/14107
Enthalten in
Proceedings of SPIE 
Volume
10394
Article Number
1039419
Citation
Wavelets and Sparsity (2017)
Contribution to Conference
Wavelets and Sparsity, 2017 
Publisher DOI
10.1117/12.2275547
Scopus ID
2-s2.0-85033579531
The product of Gaussian random variables appears naturally in many applications in probability theory and statistics. It has been known that the distribution of a product of N such variables can be expressed in terms of a Meijer G-function. Here, we compute a similar representation for the corresponding cumulative distribution function (CDF) and provide a power-log series expansion of the CDF based on the theory of the more general Fox H-functions. Numerical computations show that for small values of the argument the CDF of products of Gaussians is well approximated by the lowest orders of this expansion. Analogous results are also shown for the absolute value as well as the square of such products of N Gaussian random variables. For the latter two settings, we also compute the moment generating functions in terms of Meijer G-functions.